Timeline for What's "serialization" really called, and is there any theory surrounding it?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2017 at 15:41 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Jul 2, 2017 at 15:26 | comment | added | Max | You should really change the notation here, is the operator aplied to the whole family of sets? or is it just applied to the sets whose index is lower than some fixed $i$ ? It makes it unnecessarily more difficult to understand. | |
| Jul 2, 2017 at 15:18 | comment | added | Michael Greinecker | And in some cases where you actually do care about the order, the notion is ill-behaved. The limit superior of a sequence is the limit (usual order) of the "anti-serialization" (serialization under the dual order) of the sup-operator. Without seeing some interesting argument applying to all serializations, I don't see why one should expect a general theory. | |
| Jul 2, 2017 at 15:18 | comment | added | Michael Greinecker | In many cases, the ordering of the index set is just a crutch. For absolutely convergent sequences, the infinite sum is more naturally defined as the limit of all finite sums given the net of finite subsets. The same applies even to the "disjointification trick" in many applications in measure theory. | |
| Jul 2, 2017 at 15:11 | comment | added | Joel David Hamkins | Sorry, I meant $\vec\bigcup_{i\in\mathbb{Z}}A_{i+1}$ and $\vec\bigcup_{i\in\mathbb{Z}}A_i$ in the previous comment. | |
| Jul 2, 2017 at 15:09 | answer | added | Joel David Hamkins | timeline score: 3 | |
| Jul 2, 2017 at 15:01 | comment | added | Joel David Hamkins | Suppose I want to evaluate the $i=2$ instance of your expression $\vec\bigcup_{i\in I}A_i$. Can I write $\vec\bigcup_{i\in I}A_2$? I don't think so. Suppose that I re-index by one; what does $\vec\bigvee_{i\in \mathbb{Z}}A_{i+1}$ mean, as opposed to $\vec\bigvee_{i\in I}A_i$? | |
| Jul 2, 2017 at 14:50 | comment | added | goblin GONE | @JoelDavidHamkins, I think what you're saying is equivalent to the position that $\frac{\partial}{\partial x} E$ could be improved by changing it to $(D(\lambda x.E))(x')$ or some such, which I don't really agree with. But I'm happy to hear you out. Can you give more details about these ambiguous expressions? What's a simple example of such a thing? | |
| Jul 2, 2017 at 14:47 | comment | added | Joel David Hamkins | It seems to me that the notation could be improved, since the subscript $i$ gives $i$ the appearance of a bound variable, with the $A_i$ appearing under its scope, as in $\vec\bigcup_{i\in I}A_i$, but that is not what you mean, since you indicate that the output is something that depends on $i$. One can easily manufacture ambiguous expressions with this kind of notation. It seems to me that what $\vec\bigcup$ should really output is a function from $I$ to those instances. | |
| Jul 2, 2017 at 14:36 | history | edited | goblin GONE | CC BY-SA 3.0 |
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| Jun 29, 2017 at 9:09 | history | asked | goblin GONE | CC BY-SA 3.0 |